What are the types of complex iteration and tetration?

[Daniel]

For using complex tetration with a fixed point at imaginary infinity consider that the further the fixed point is from the real axis, the greater the dampening of the complex oscillations. But the dynamics of the complex tetration with a fixed point at imaginary infinity must be the same as that of the next further out fixed point. Since the further fixed point must dampen the oscillations even more, and yet be the same as the previous fixed point, the only feasible scenario is if the oscillations are complexly dampened out and we are looking at real tetration. Unfortunately I'm having troubles thinking of a constructive approach that provides actual values.